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www.shapeoperator.com | ||
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terathon.com
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| | | | | [AI summary] The provided text is a detailed critique of the book 'Projective Geometric Algebra' by the authors, highlighting numerous errors and misunderstandings in their treatment of geometric algebra, particularly in areas such as norms, duality, and the Hodge dual. The author of the critique points out that the book's definitions and explanations are often incorrect, misleading, or based on flawed reasoning. Key issues include the misuse of the Hodge dual, incorrect definitions of norms, and a lack of understanding of fundamental concepts like operator duality and the relationship between different types of norms. The critique also addresses the authors' attempts to compare the efficiency of PGA operators with matrices, which are shown to be misleading.... | |
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alexkritchevsky.com
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| | | | | [AI summary] The article critiques Geometric Algebra (GA) for its reliance on the geometric product, which the author finds problematic for most purposes. The author argues that GA's focus on complexifying vector algebra to resemble complex numbers and quaternions is unnecessary and confusing. Instead, the author advocates for a simpler approach using exterior algebra and wedge products, emphasizing clarity and intuition over abstract algebraic structures. The author also mentions the philosophical and pedagogical issues with GA, such as its conflation of operators and primitives, and the cultural baggage associated with the term 'Geometric Algebra.' The article concludes by suggesting that while GA has value as an implementation detail, it should not be see... | |
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mattferraro.dev
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| | | | | In this post we will re-invent an obscure form of math that is far superior to the one you learned in school. It is a better foundation for science and engineering, and it is a better foundation for students. | |
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terrytao.wordpress.com
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| | | [This post is dedicated to Luca Trevisan, who recently passed away due to cancer. Though far from his most significant contribution to the field, I would like to mention that, as with most of my ot... | ||
